An asteroidal triple (AT) is a set of vertices such that each pair of vertices is joined by a path that avoids the neighborhood of the third. Every AT-free graph contains a dominating pair, a pair of vertices such that for every path between them, every vertex of the graph is within distance one of the path. We say that a graph is a hereditary dominating pair (HDP) graph if each of its connecte...

A linear theory for the heat conduction in a spherical, solid and rotating body illuminated by solar radiation is developed in detail. The principal aim is to compute the recoil force, due to thermally reemitted radiation, which is commonly known as the “Yarkovsky force”. We concentrate on the thermal effect which depends on the rotational period of a body rather than on the period of revolutio...

Various families of tolerance graphs of subtrees for specific families of host trees and tolerance functions have been successfully characterized. For example, chordal graphs are intersection (tolerance 1) graphs of subtrees of general trees, see [2], [5], and [8]. Intersection graphs of subtrees of a path are those that are chordal and do not contain an asteroidal triple, see [7]. We denote by...

An asteroidal triple is an independent set of three vertices in a graph such that every two of them are joined by a path avoiding the closed neighborhood of the third. Graphs without asteroidal triples are called AT-free graphs. In this paper, we show that every AT-free graph admits a vertex ordering that we call a 2-cocomparability ordering. The new suggested ordering generalizes the cocompara...